We show that each perfect matching in a bipartite graph $G$ intersects at least half of the perfect matchings in $G$. This result has equivalent formulations in terms of the permanent of the adjacency matrix of a graph, and in terms of derangements and permutations on graphs. We give several related results and open questions.

中文翻译：

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图上的完美​​匹配和排列

我们证明了二分图中的每个完美匹配 $G$ 与至少一半的完美匹配相交 $G$。就图的邻接矩阵的永久性以及图的排列和排列而言，此结果具有等效的表示形式。我们给出一些相关结果并提出未解决的问题。